Non-platonic solid graphs.

Question

My teacher gives me a task : find all simple(without loops) connected graphs with $d \ge 3$ - degree of all vertices and $k \ge 3$ - number of edges , which cover any field. I build all possible cases $(3;3),(4;3),(3;4),(5;3),(3;5)$ - all platonic graphs. But he also asked about graphs with loops and tuple-edges and $d \ge 3$, $k \ge 3$. I've found some special cases, when $d = 3$ and $k = 3$. Does there some general constructions?